Finding Zeros of Quadratic Functions: Factoring the Difference of Two Squares

This lesson teaches how to find the zeros of a quadratic function by factoring the difference of two squares. It explains the concept of the difference of two squares, provides examples, and addresses common misunderstandings. The lesson also demonstrates how to find zeros of quadratic functions using the zero product property and verifies solutions by substitution.

What is the result of factoring the expression 25x squared minus 49?

• (5x - 7)(5x + 9)

• (5x - 7)(5x - 7)

• (5x + 7)(5x - 7)

• (5x + 7)(5x + 7)

Which of the following is a common mistake when factoring x squared minus 16?

• Factoring as (x + 4)(x + 4)

• Factoring as (x + 4)(x - 4)

• Factoring as (x - 4)(x - 4)

• Factoring as (x - 4)(x + 4)

What is the correct factorization of x squared minus 16?

• (x + 4)(x - 4)

• (x - 8)(x + 8)

• (x - 4)(x - 4)

• (x + 4)(x + 4)

What are the zeros of the function f(x) = x squared minus 81?

• -7 and 7

• -8 and 8

• -6 and 6

• -9 and 9

How do you find the zeros of f(x) = x plus 1 times x minus 1 minus 8?

• Set the function to zero and factor as (x + 5)(x - 5)

• Set the function to zero and factor as (x + 2)(x - 2)

• Set the function to zero and factor as (x + 4)(x - 4)

• Set the function to zero and factor as (x + 3)(x - 3)